Problem 14 · 2009 Math Kangaroo
Medium
Geometry & Measurement
perimeter
The “tower” in the diagram is made up of a square, a rectangle and an equilateral triangle. Each of these three shapes has the same perimeter. The side length of the square is 9 cm. How long is the marked side of the rectangle?
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Answer: C — 6 cm
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Hint 1 of 2
All three shapes share one perimeter — find it from the square first.
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Hint 2 of 2
The triangle's side fixes the rectangle's long side; use the shared perimeter to get the other side.
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Approach: equal perimeters
- The square has side 9, so its perimeter is 4 × 9 = 36; every shape has perimeter 36.
- The equilateral triangle has side 36 ÷ 3 = 12, which is the rectangle's longer side.
- The rectangle's perimeter 2(12 + h) = 36 gives h = 6.
- So the indicated side of the rectangle is 6 cm — answer C.
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